Customer Reviews

Nonlinear Systems

5 star:		(7)
4 star:		(4)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

Hassan Khalil's book (already in its second edition) has become a best-seller. Easy to understand why.

At the same time, the text manages to be very readable and fairly sophisticated. In fact, it is not very usual for Engineering texts to display such an advanced level of mathematical rigor. As a result, however, it is not entirely true that the book can be easily followed by undergrads. A reasonable degree of familiarity with -- or, rather, dexterity in -- the basics of Mathematical Analysis (with some topological underpinnings) is required. But, since the book is filled with theorems and rigorous proofs galore, grad students and research engineers with a strong penchant for Math are bound to welcome it as a bona fide blessing!

Unfortunately, it must be said that the book fails to make the 5-star rating for two reasons. First off, it is perhaps a bit too Electrical-Engineering-geared, nearly ignoring examples from other fields. Secondly, its treatment of time-varying systems is rather scanty, at best, basically relying on what can be ultimately traced to the intelectually dissatisfying time-freezing approach. (This is probably justifiable, since it would otherwise imply an additional 40-50 pages to make room for operator theory and Hilbert spaces, as is done, e.g., in the book by Feintuch & Saeks.)

Nevertheless, Prof. Hassan's is by far one of the best texts currently on the market.

This is an excellent textbook, outdoing, AS SUCH, the books by Vidyasagar, Isidori, and Rugh, as well as both of Minorsky's related classics. It is well written, well balanced, making extensive use of a fairly sophisticated language (not too abstract but certainly far from archaic), and features a plethora of exercises of various difficulty levels. Appendix A, presenting detailed, careful proofs of 21 theorems and lemmas is a definite "must." This appendix alone is worth the (sour) price of the book, making it today's "text of choice" when it comes to teaching courses. (Students should be familiar with ALL of them!)

The topics dealt with, while, for the most part, pretty standard, are appropriate for a first graduate course on nonlinear systems, as approached from the Control Engineering viewpoint. There's a bit of just about everything that's important in present-day studies of such systems: mathematical foundations, stability analysis, periodic solutions, averaging & pertubations (both regular and singular), feedback control & linearization, and Lyapunov-based design, including adaptive control. Even H-infinity is touched in passing!

Unfortuantely, the famous conjectures by Aizerman and Kalman and Letov's contributions do not constitute a central interest in the book. Lur'e's problem, on the other hand, IS mentioned.

The author provides a 195-title reference list and an effort to include recent texts is apparent. However, a few serious omissions do occur. For instance, Russian publications are nearly non-existing on said list, and Desoer's famous 1969 paper on the stability of slowly-varying systems is not mentioned explicitly. But it is not entirely accurate to say that Khalil's treatment of time-varying systems is centered around time-freezing techniques. He does, indeed, present one or two examples to that effect. But out of 734 pages, no less than 16 are dedicated to several aspects relating to stability of time-varying systems, most of which can be directly mapped back to Desoer's theorem.

By and large, this book is -- and shall remain for some time to come -- the best text for introductory graduate courses in Nonlinear Systems.

Being a Ph.D. canidate in Control Theory at Georgia Tech, I am familiar with the essential tools needed to be sucessful in advanced control engineering. This book covers the entire spectrum of topics in control theory presented at many universities around the country. It is presented with a strong mathematical foundation and has many illustrative examples. Subjects covered include the fundamental properties of differential equations, basic and advanced stability theory, feedback control and the feedback linearization/computed torque method which is a very popular approach to nonlinear design. It also contains introductions to newer techniques such as adaptive and sliding mode control. In my studies at GT, i have more than once been plesently suprised to find tools in this book that i didnt expect to find there. For example, chapters 5-9 cover the improtant results that i was exposed to in a 3 course graduate level sequence in ODE's from the math department!!

This book is sugessted for any serious student of control theory and it is recommended that the reader be exposed to at least one introductory real analysis course.

This book is the most easy to understand, yet rigorously written nonlinear systems book on the market. It is very suitable for those interested in nonlinear controls. This book is also good as a reference book on nonlinear systems topics. The level of mathematical complexity matches the level of Ph.D. students, although it is sometimes difficult to follow.

This book is excellent both as a textbook and as a referencemonography (it is in fact widely referenced in the literature). It isvery readable (at the level of Hirsch & Smale's classic "Differential equations, dynamical systems, and linear algebra"), and definitely accessible to undergraduates with some previous knowledge of ODEs. The first two chapters cover the basics (existence/uniqueness/continuation of solutions, motivating examples). Lyapunov's theorems and their applications are the core of the book, and are very carefully explained. The author covers autonomous/nonautonomous systems and the related invariance theorems; converse Lyapunov theorems, perturbed systems, input-output stability (very welcome here); stability of periodic orbits; perturbation theory. Many theoretical results are illuminated by examples. Researchers with an interest in robust control and stability of dynamical systems will find this book useful. The only reason for giving 4 stars to this book is its price. END

As far as most grad level controls textbooks go, this one is pretty decent. The theorems have some examples, and the proofs are put in the appendix for good continuity.

Used this for a Nonlinear Control Theory Class. It was a little short on Control Theory (didn't include much adaptive control etc) but has such good coverage of nonlinear stability theory that it is extremely applicable for a Control Theory class. Does a great job explaining complicated ideas, and does a spectacular job providing references for more information.

This book won the IFAC Control Engineering Textbook Prize in 2002, but its greatness can more accurately be established by simply noting that it is used as THE nonlinear controls textbook by many engineering departments.

The third edition contains material about high gain observers and sliding modes which are welcome additions. The book also contains sections about backstepping and passivity techniques. As in the first edition the author's writing is clear and concise. It is a good complement to Vidyasagar's Nonlinear Systems book.

A good textbook for nonlinear system design, I am using it for a graduate NL control design course. Gives a thorough treatment of Lyanpunov stability and applications, as well as NL design techniques. The text is on the mathematical side, a good companion to 'Applied Nonlinear Control' by Li and Slotine.

This book offers a deep explanation about the stability foundation regarding Lyapunov Theorem. It is strongly advisable this book for any researcher who is intending to follow this filed of work.